What was the next number or numbers that you KNEW had to go and where did you place them??
I mean I know r1c1 c2 c3 had to be a combo of 5 3 9, but if you are telling me that the solution does not demand a definite position for these, how did you figure that out?

I have lost myself a lot of time with so called "Sudoku"s which do not have unique solutions.

BE AWARE THAT THERE ARE SUCH SITES IN THE INTERNET, NOT WARNING YOU THAT THEY PUBLISH PUZZLES WITH MULTIPLE SOLUTIONS.

You have 2 options:
- a quick and clean or
- a long and durty
- a wise

The quick and clean, is to use a program. I suggest even for this page to include one that is JUST telling us (using even brute force) that this puzzle has multiple solutions. Or an option to the existing one.

The long and durty, is to find out by yourself. You will need "try and error" technique. Which is durty, durty, durty bad boy

I stared at your puzzle for about 10 minutes, trying to see a pattern. You had kindly provided the list of candidates for each cell, which sped things up a lot for me. Anyway, when I couldn't see any useful clues, I fed the puzzle to a computer program, which informed me that multiple solutions exist.

Daykart wrote:

What was the next number or numbers that you KNEW had to go and where did you place them??

I didn't KNOW where any more numbers had to go. So I just guessed. I focused on the {1, 2} pair appearing in r1c5 & r1c8 -- it was obvious, and offered good possibilities for finding two different solutions. First I tried placing a "1" at r1c8 -- the computer program informed me that 19 solutions were possible. Then I put a "2" at r1c8, and the computer said there were 8 possible solutions.

After that I didn't much care about logical niceties -- I just bashed away at the puzzle using brute force to find two of the 27 possible solutions. (The program I'm using will count the number of possible solutions, but it won't display them all.)

Daykart wrote:

I mean I know r1c1 c2 c3 had to be a combo of 5 3 9, but if you are telling me that the solution does not demand a definite position for these, how did you figure that out?

I just used trial and error (plus the computer program) from the initial placement of either "1" or "2" I had made at r1c8. As it turned out, the particular "solutions" I was able to construct contain the {3, 5, 9} triplet in two different orders. Maybe there are two "solutions" that interchange the "1" and "2" at r1c8 without altering the order of the {3, 5, 9} triplet. I don't know -- and I don't really care.

For me, the important thing is knowing that a puzzle has a unique solution. If it does, then a "logical" route to that unique solution is possible, at least in principle. But when multiple "solutions" exist, the only way to find them is by guessing, and that's no fun. dcb

For me, the important thing is knowing that a puzzle has a unique solution. If it does, then a "logical" route to that unique solution is possible, at least in principle. But when multiple "solutions" exist, the only way to find them is by guessing, and that's no fun.

100% agree with you.

I am/would start with a program to check, if there is a unique solution, even before dealing with the puzzle, if I don't trust the source that has published it.

Like the german are used to say: "Vertrauen is gut, aber Kontrolle ist besser" - meaning "Confidence is good, but checkup is better".

> It is no wonder you can't make progress.
> This puzzle has 27 solutions!

> How did you determine so fast that there were multiple solutions?

> I fed the puzzle to a computer program, which informed me
> that multiple solutions exist. (The program I'm using will count
> the number of possible solutions, but it won't display them all.)

Who publishes this program?
Does it include 'trial and error' in its solution logic?
Other topics on this site suggest that it is almost impossible to
GUARANTEE to find one solution (let alone several!) without
resort to trial and error in some cases.

> For me, the important thing is knowing that a puzzle has
> a unique solution. If it does, then a "logical" route to that
> unique solution is possible, at least in principle. But when
> multiple "solutions" exist, the only way to find them is by
> guessing, and that's no fun.

Agreed, absolutely!!!

> I would start with a program to check, if there is a unique
> solution, even before dealing with the puzzle, if I don't
> trust the source that has published it.

This sounds like a sad overhead. I use the computer as a
print device (DRAW) but after my first couple of months
learning about Sudoku I do not otherwise use the computer
in any way. As SamGJ states in the site introduction (FAQ)
"What's the point?" of devising solvers.

Having said that, the art of COMPILATION is a complete mystery
to me. Are there books on this aspect of Sudoku? I can see that
computers could be helpful with this until one has got to grips
with the processes - including ensuring uniquity!